Question

How do you solve `(3/4)^(2x) = 64/27`?

Answer 1

`x=-5,3188416645`

Explanation:

`(3/4)^(2x)=64/27`
`(3/4)^(2x)=2^6/3^3`

`3^(2x)/4^(2x)=2^6/3^3`

`3^(2x)*3=4^(2x)*2^6`

`3^(2x+1)=2^(4x)*2^6`

`3^(2x+1)=2^(4x+6)`

`log 3^(2x+1)=log 2^(4x+6)`

`(2x+1)*log 3=(4x+6)*log 2`
`log 3=0,47712125773`
`log 2=3010299957`
`(2x+1)*0,47712125773=(4x+6)*0,3010299957`
`0,9542425094x+0,47712125773=1,2041199827x+1,806179974`
`0,2498774733x=-1,329058716`

`x=-5,3188416645`